Answer:
[tex]\large\boxed{x=20}[/tex]
Step-by-step explanation:
The whole triangle and small triangle are similar (AA). Therefore the sides are in proportion:
[tex]\dfrac{5x+10+10}{10}=\dfrac{121+11}{11}[/tex]
[tex]\drac{5x+20}{10}=\dfrac{132}{11}[/tex] cross multiply
[tex]11(5x+20)=(10)(132)[/tex] use distributive property
[tex](11)(5x)+(11)(20)=1320[/tex]
[tex]55x+220=1320[/tex] subtract 220 from both sides
[tex]55x=1100[/tex] divide both sides by 55
[tex]x=20[/tex]
